Research on Bending Wave Regulation Mechanism and Integrated Vibration Attenuation and Energy Harvesting Characteristics of Graded Piezoelectric Metamaterial Beams

This paper investigates the graded piezoelectric metamaterial beam as the research subject, conducting an in-depth analysis of the bending wave regulation mechanism and its dual-function capabilities for vibration attenuation and energy harvesting. First, a theoretical model of the graded piezoelectric metamaterial beam is established to examine how different grading schemes govern the structural parameters of individual segments within each unit cell. Second, the transfer matrix method is employed to compute the band structures, thereby elucidating the propagation characteristics of bending waves and the underlying energy harvesting mechanisms across various graded configurations. Subsequently, a quantitative evaluation index tailored to the dual-function performance—vibration attenuation and energy harvesting—is proposed to reveal the influence of grading order on frequency-band broadening and overall performance metrics. Finally, the theoretical findings are validated via finite element (FE) simulations. The results demonstrate that the graded piezoelectric metamaterial beam induces a spatial frequency division effect in bending waves and enables localized concentration of wave-field energy. Compared with the non-graded counterpart, the graded configuration simultaneously achieves vibration attenuation and energy harvesting over a low-frequency broadband range. Among these configurations, the fractional-order and first-order graded designs exhibit the most pronounced enhancement of overall dual-function performance.